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S. Odate, C. Koike, H. Toba, T. Koike, A. Sugaya, K. Sugisaki, K. Otaki and K. Uchikawa, “Angular Spectrum Calculations for Arbitrary Focal Length with a Scaled Convolution,” Optics Express, Vol. 19, No. 5, 2011, pp. 14268-14276. http://dx.doi.org/10.1364/OE.19.014268

has been cited by the following article:

• TITLE: Optimal VIA Placement in Under Filled Embedded Multimode Waveguides

  AUTHORS: Nicholas Riegel, Matthew Howard, Christopher Middlebrook

  KEYWORDS: Multimode Optical Waveguides; Optical Vertical Interconnect Assembly

  JOURNAL NAME: Optics and Photonics Journal, Vol.3 No.6, October 22, 2013

  ABSTRACT: The self-imaging property of multimode waveguides creates a challenging problem when finding the optimal placement position of an out-of-plane coupler for embedded waveguides. This problem is compounded when the waveguides are coupled using a small input such as a vertical cavity surface emitting laser (VCSEL) or a single mode fiber where only some of the modes are generated. When the waveguide system is under filled, the coupling efficiency for the optical vertical interconnect assembly (VIA) can vary by as much as 6.2 dB depending on the length of the proceeding waveguide due to different output fields from the self-imaging property. This requires sweeping each individual VIA over the entire range of possible coupler positions to find the total maximum coupling efficiency. This process increases in complexity when a VIA supports several parallel channels all having a different optical path length. If a VIA can be placed in a calculated position from the end of a terminated embedded waveguide dependent upon the modal structure then blind pick and place methods may be used. The optimal coupler placement was determined based on smallest average VIA attenuation, smallest attenuation variance, and worse-case alignment scenario.